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In a certain library the first shelf is 12.0$\mathrm { cm }$ off the ground, and the remaining 4 shelves are each spaced 33.0$\mathrm { cm }$ above the previous one. If the average book has a mass of 1.40$\mathrm { kg }$ with a height of $22.0 \mathrm { cm } ,$ and an average shelf holds 28 with a height of $22.0 \mathrm { cm } ,$ and an average shelf holds 28 books (standing vertically), how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start?

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$$W \approx 1710.0 \mathrm{J}$$

Physics 101 Mechanics

Chapter 7

Work and Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

McMaster University

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7.71. So we're in a library and we have a shelf that's, uh, 12 centimeters off the ground. And then each subsequent shelf is 33 centimeters above the previous one. They're five shelves in total. And so we want to know what the total work is required to filthy shells. Each one holds 28 books, assuming that a book is 22 centimeters tall and has a massive 1.4 kilograms and the books start off lying flat on the floor. So the Sardo work, her book is going to be the weight of the book, uh, times the height at center of, uh, at center of mass moves. So, um half. So we're going to have its gonna move half the height of the book to be moved up, right, and then the distance from the floor to the shelf. It's currently on. So to move 28 books to the first shell, 28 of them have the weight of the book. And so 11 centimeters plus 12 centimeters cause 11 centimeters is the height to the center of mass. Of the book is 23 centimeters. Um, well and then we can continue on. You know what this train of thought? You 28 mg fines. What, 23 meters than the second shelf will be 0.56 meters. The third show, Uh, 0.89 meters off 1.22 meters plus 1.55 meters. So the total work done to fill all of these shows is 1710 Jules.

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